ECE 321
Exam 1 SolutionSpring 2006
Problem 1
Relative permeability is a dimensionless scaling factor,
µ
r
, that indicates how permeable
a material is with respect to free space, i.e.
µ
material
µ
r
µ
0
⋅
=
Problem 2
flux density: B (T or Wb/m^2)
field intensity: H (At/m)
Problem 3
Ferrimagnetic
Problem 4
Hysteresis
Problem 5
No.
The mixed partials are not equal.
i
2
λ
1
∂
∂
7
=
i
1
λ
2
∂
∂
6
=
(Problem 6)
Ignore.
Does not exist.
Problem 7
Field energy
Problem 8
L
abs
λ
i
=
20i
2
i
=
20
=
H
L
inc
i
λ
∂
∂
=
40i
=
40
=
H
Problem 9
T
θ
rm
W
c
∂
∂
=
8
−
1
e
i
1
i
2
+
(
)
−
−
⎡
⎣
⎤
⎦
⋅
sin 4
θ
rm
(
)
=
Problem 10
Step 1:
i
2
0
=
W
1
i
1
λ
1
⌠
⎮
⎮
⌡
d
i
2
λ
2
⌠
⎮
⎮
⌡
d
+
=
0
i
1
i
1
5
i
1
⋅
10
1
x
2
+
1
e
5
−
i
1
⋅
−
⎛
⎝
⎞
⎠
⋅
+
⎡
⎢
⎢
⎣
⎤
⎥
⎥
⎦
⌠
⎮
⎮
⎮
⌡
d
=
W
1
5i
1
2
2
10
1
x
2
+
i
1
e
5
−
i
1
5
+
⎛
⎜
⎝
⎞
⎠
i
1
0
=
i
1
,
⋅
+
=
5i
1
2
2
10
1
x
2
+
i
1
e
5
−
i
1
5
+
1
5
−
⎛
⎜
⎝
⎞
⎠
⋅
+
=
Step 2:
i
1
constant
=

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*